Solved my own problem and thought I'd post the solution here in case anyone else runs into this problem and is searching Google for an answer.
If you enable the IO APIC option under General settings, this problem goes away. I'm not sure if I changed it or the default setting changed in 2.0.6, but in either case, just Enable the IO APIC option (select your VM, hit the Settings button at the top, go the Advanced tab, and select the Enable IO APIC checkbox under Extended Features), and Virtual Box will save and shut down cleanly without getting to the dread Aborted state.
Cheers.
Just thought I'd post and let everyone know I am having a similar problem, but the above [for me at least] isn't a fix-- I have had IO APIC already turned on since install, and this is still happening. So give the fix a try, but if you're like me and already have that setting checked, then there must be some additional problem going on. I'll post again if I figure it out.

WARNING: Do NOT UNcheck the IO APIC if you installed with it checked!! Windows will freak out! At least, that's what the VirtualBox docs say-- I haven't tried it myself...

UPDATE:
Mysteriously, I just now had one successful save machine state-- it made it all the way through the progress bar, and listed the state as "Saved". I did not change anything to cause it. However, it also crashed on resume, once again listing as "Aborted". Thoughts, anyone?
